Conn. Gen. Stat. § 52-235b: Proceedings stayed if attorney unable to appear.

If, prior to judgment, an attorney for any reason ceases to be a member of the bar or becomes physically or mentally incapacitated or otherwise disabled so as to prevent him from appearing in court in an action in which he has appeared for a client, further proceedings shall not be taken in the action against the client, without leave of the court, until thirty days after notice to appear in person or by another attorney has been served upon the client either personally or in such manner as the court directs.